Prediction of bus arrival time is an important part of intelligent transportation systems. Accurate prediction can help passengers make travel plans and improve travel efficiency. Given the nonlinearity, randomness, and complexity of bus arrival time, this paper proposes the use of a wavelet neural network (WNN) model with an improved particle swarm optimization algorithm (IPSO) that replaces the gradient descent method. The proposed IPSO-WNN model overcomes the limitations of the gradient-based WNN which can easily produce local optimum solutions and stop the training process and thus improves prediction accuracy. Application of the model is illustrated using operational data of an actual bus line. The results show that the proposed model is capable of accurately predicting bus arrival time, where the root-mean square error and the maximum relative error were reduced by 42% and 49%, respectively.

In reliability analysis, degradation test has been recognized as an effective method for high reliable products and complex systems when key performance indicators can be observed. Then, a reasonable degradation model becomes a key issue to guarantee a reasonable reliability assessment. Motivated by practical needs, this paper proposes a novel two‐stage degradation model considering the different dispersity regulations corresponding to the two stages. A maximum likelihood estimation (MLE) method for unknown parameters is established, and an initial guess procedure is given to improve the efficiency of optimization algorithm. Then, the reliability inference regarding the product population is discussed. A comprehensive simulation study is conducted to validate the proposed approach where the two‐stage Wiener process model is adopted as a reference for a better understanding. Finally, the constructed model is further verified by two real applications. Comparative results clearly demonstrate the reasonability and effectiveness of the proposed model.

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